Rep. Anthony Weiner said yesterday he will take on Mayor Bloomberg if he runs for a third term, while two other leading Democrats were on the fence.

“Anthony is celebrating Rosh Hashana, but has said he is running for mayor. He wants to offer a vision of how to fight for the middle class and those struggling to make it,” Weiner spokesman John Collins said. He called the mayor’s plans to seek four more years “highly speculative” because there’s been no change to the existing law limiting officials to two terms.

But with Bloomberg on board, most City Hall insiders believe the City Council will easily pass such a bill, particularly since 34 of the 51 would be term-limited out of office last year.

Council Speaker Christine Quinn, a potential mayoral candidate, was mum on the issue yesterday and City Comptroller William Thompson, another prospect, sat on the fence.

Quinn’s staff did not respond to repeated requests for comment after news broke in the afternoon that Bloomberg intends to announce plans tomorrow that he will run for a third term.

The speaker previously blasted the prospect of “overruling the will of New Yorkers” on term limits through a bill, instead of a public referendum, but has backed off her criticism in recent months.

Thompson was vague about his own plans, though he blasted the possibility of a legislative change to term limits. “Right now the law says that there are two terms. It is my intention to run for mayor next year,” Thompson told The Post. But, he added, it is “too early” to decide whether he would challenge Bloomberg. “Let me see what he does and then I’ll start to make decisions.”

Weiner, who represents Queens and Brooklyn, is the only one of the potential Dem candidates to have run for mayor before. He dropped out of the 2005 primary runoff after finishing behind Fernando Ferrer in the first round.

Councilman Tony Avella (D-Queens) said he would run for mayor next year, regardless of the mayor’s plans.

Republican billionaire John Catsimatidis, who owns Gristedes supermarket, did not say whether he would stay in the mayoral race. GOPer Bruce Blakeman – the only officially declared candidate other than Avella – announced yesterday he would not challenge Bloomberg, an independent.

Meanwhile, former Mayor Rudy Giuliani, who asked for a 90-day extension in office to deal with the 9/11 attacks, praised the mayor but wouldn’t commit backing him for a third term.

“He is somebody that I admire and my whole issue is the good of the city,” he added, when asked if he would support Bloomberg.

Kathryn Wylde, president of the Partnership for New York City and a Bloomberg ally, encouraged Bloomberg to run.

“The business community urges the City Council to go forward with legislation to extend term limits by four years,” she said. “New York City and the country face a serious economic crisis and continuity in leadership is crucial at this time.”